Cartan型广义李超代数(英文)

Generalized Lie Superalgebras of Cartan Type

英文关键词:generalized Lie superalgebra, Grassmann algebra

中文摘要:

      设F是特征不为2的域.本文定义了F上的广义李超代数，证明了Z-阶化广义李超代数的单性准则.然后定义了有限维Cartan型广义李超代数W(n),证明了W(n)的单性.最后指出对Cartan型广义李超代数S(n)与H(n)，亦有与W(n)相似的结果.

英文摘要:

      Let F be a field of characteristic p≠2. In this paper, we define the generalized Lie superalgebra over F and prove the criterion of simplicity of a Z-graded generalized Lie superalgebra. We give the definition of the finite dimensional Cartan generalized Lie superalgebra W(n) and prove the simplicity of W(n). Finally, for Cartan generalized Lie superalgebras S(n) and H(n),we give the same result as for W(n).